Reversible Diffusion-Limited Reactions: "Chemical Equilibrium" State and the Law of Mass Action Revisited

TL;DR

This paper critically examines the concepts of chemical equilibrium and the law of mass action in reversible diffusion-limited reactions, demonstrating that the asymptotic state is generally a non-equilibrium steady-state and that classical laws do not hold in realistic scenarios.

Contribution

It provides an exact analytical analysis showing that reversible diffusion-limited reactions do not generally reach true equilibrium and that the law of mass action is invalid in such cases.

Findings

Asymptotic state is a non-equilibrium steady-state.

Law of Mass Action is generally invalid for diffusion-limited reactions.

Classical equilibrium only holds under unrealistic reaction probability conditions.

Abstract

The validity of two fundamental concepts of classical chemical kinetics - the notion of "Chemical Equilibrium" and the "Law of Mass Action" - are re-examined for reversible \textit{diffusion-limited} reactions (DLR), as exemplified here by association/dissociation $A+A \rightleftharpoons B$ reactions. We consider a general model of long-ranged reactions, such that any pair of $A$ particles, separated by distance $\mu$, may react with probability $\omega_+(\mu)$, and any $B$ may dissociate with probability $\omega_-(\lambda)$ into a geminate pair of $A$s separated by distance $\lambda$. Within an exact analytical approach, we show that the asymptotic state attained by reversible DLR at $t = \infty$ is generally \textit{not a true thermodynamic equilibrium}, but rather a non-equilibrium steady-state, and that the Law of Mass Action is invalid. The classical picture holds \text{only} in physically unrealistic case when $\omega_+(\mu) \equiv \omega_-(\mu)$ for any value of $\mu$.